I'm assuming that anchoring while fishing means the you will have lookout all the time and that you will be able to act immediately if you start dragging.
I would think that going smaller than 1/2" rope would be harder on the hands?
There are two reasons to use chain at the anchor end
- Chain is more resilient against chafe than rope
- Chain give better catenary
It's not uncommon around here to have all rope rode, the life length of the rope depends on the ground where you anchor.
Some boats use braided anchor rope with lead core.
One option:
Replace the chain with dyneema - less expensive than replacing all. The Dyneema part should withstand chafe better than nylon.
The loss of weight can be compensated (partly) using more scope.